All Questions
Tagged with nonparametric regression
170
questions
2
votes
1
answer
92
views
Non-Parametric Regression with an Omitted Variable
Suppose we use the Kernel Regression Estimator $$\hat{m}(c)=\frac{\sum_{i=1}^n K\left(\frac{x_i-c}{h}\right)y_i}{\sum_{i=1}^n K\left(\frac{x_i-c}{h}\right)}$$
where $h\to 0$ and $nh\to \infty$ as $n\...
- 428
2
votes
0
answers
66
views
Linear model for maximizing rank correlation between observed and predicted response
linear regression is modelled as
$$Y = X\beta + \epsilon$$
for response variable $Y$ (vector), design matrix $X$, and iid Gaussian noise $\epsilon$ (vector).
instead of minimizing the mean squared ...
- 2,480
5
votes
0
answers
27
views
Are these two estimated regression coefficient asymptotically equivalent? If not, which one is more efficient?
Suppose I have $Y=\beta_1X_1+\beta_2X_1X_2+g(X_2)+u$, where $E(u|X_1,X_2)=0$ and $S=g(X_2)+e$ with $E(e|X_2)=0$. I have a random sample $\{Y_i,X_{1i},X_{2i},S_i\}_{i=1}^n$. Suppose I first use a ...
- 2,966
0
votes
1
answer
56
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Non-Parametric Test for Regression Significance
I have created a plot of the regression slope of sea surface temperatures (x) and an atmospheric variable (y). Although, I need to test the statistical significance of these trends using a non-...
1
vote
1
answer
111
views
OLR for non-normal continuous dependent variable with two categorical independent variables?
ID
Sex
Surface
B1
1
female
UN
1255
2
female
UN
542
3
female
UN
818
1
female
UN
274
2
female
UN
261
3
female
UN
314
1
female
UP
552
2
female
UP
548
3
female
UP
721
1
female
UP
431
2
female
...
- 11
1
vote
0
answers
171
views
Projection pursuit regression
Projection pursuit regression (PPR) is described in Hastie et al.'s The Elements of Statistical Learning in the chapter on neural networks. The algorithm was introduced by Friedman and Stuetzle (1981)....
- 751
1
vote
1
answer
115
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Multiple Linear regression unmet assumptions, what can I do?
I need your help with some work I am doing.
Some context first:
I am writing a dissertation for my master. The topic is about perceived trust in Smart Home technology. I launched a survey with a ...
- 21
0
votes
0
answers
25
views
Can I use log-log OLS with no constant to measrue the relationship between two variables in a non-normal distribution?
I am trying to measure the relationship between the price of a futures-contract and the current price of the underlying asset on the day of purchasing said futures-contract. For this I have a dataset ...
1
vote
1
answer
160
views
How to use the argument stype in boot-package in R? [closed]
The stype argument in boot of R can take 3 values: "i" which is the default, "w" or "f".
What is ...
- 151
1
vote
0
answers
69
views
Gaussian Process Regression prior with observations as integrals?
Consider some standard 1d Gaussian Process Regression (GPR). Suppose you are not happy with a typical mean-zero prior away from the data and you actually want something like the derivative of the mean ...
- 312
1
vote
2
answers
71
views
which non parametric test to use? friedman or Kruskal?
I am conducting a study on textrual complexity. We fed people food (3 types) over 3 sessions and asked questions about hunger levels. 20 participants were tested during 60 trials in total. Of the 14 ...
- 11
1
vote
0
answers
128
views
Gasser Müller estimator for estimating the derivative $m'(x)$ of a nonparametric regression function
I would like to compare the performance of the Gasser Müller estimator with other estimators for estimating the the derivative $m'(x)$ of the regression function $m(x)$.
Let's say we have the ...
- 111
3
votes
2
answers
1k
views
Why is the Cox-PH Model called "Semi Parametric"?
When it comes to Survival Analysis, I understand that there are 3 main classes of models:
Non-Parametric Models
Parametric Models
Semi-Parametric Models
Non-Parametric models are like the Kaplan-...
1
vote
1
answer
241
views
Which statistical test should I use if the assumptions of a 2-way ANOVA are not met?
My study design consists of two factors (one with 2 levels, the other with 6) and a continuous response variable. In order to analyze the influence of both factors on the explanatory variable I built ...
- 441
8
votes
1
answer
178
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What do the terms "nearly-optimal rate", "near-minimax rate", "minimax optimal rate" and "minimax rate" mean in the context of posterior consistency?
Definition: A sequence $\epsilon_n$ is a posterior contraction rate at the parameter $θ_0$ if $$\Pi_n(θ: d(θ, θ_0) ≥ M_n \epsilon_n| X^{(n)}) → 0$$ in $P^{(n)}_{θ_0}$-probability, for every $M_n → ∞$.
...
- 308
1
vote
0
answers
141
views
how well would a robust mixed model fit these data? R (rlmer)
I want to investigate Y ~ X1 * X2 + (1|ID on this dataset (there's a plot of these data in that post too, it's the same dataframe)
Y is a continuos outcome ...
- 781
2
votes
1
answer
145
views
MARS vs. CART regression predictive power
I have been wondering recently about the prediction power of the two similar models: Decision Trees and the MARS model (instead of fitting the mean to the subsets, OLS line is estimated). Given that ...
- 205
1
vote
1
answer
86
views
Does the P value need to be "back- transformed" after logging one variable in Regression analyse?
I have a data series, sediment concentration in water Vs Time. The data is not normal but I want to use regression and so have logged the sediment concentration (log10(x)). The residual and fit to ...
- 11
2
votes
0
answers
26
views
Sample size planning method differs from analysis method
I have seen some articles using one method for sample size estimation(two sample comparison for means or proportions) and subsequently using regression analysis/non parametric methods.
If I have a ...
- 1,445
6
votes
4
answers
3k
views
Is there a non-parametric form of a 3-way ANOVA?
I am currently in the process of writing a publication about the home range of cat shark species in South Africa. However, I am currently struggling with how to create an interaction model of shark ...
- 61
1
vote
0
answers
23
views
Design points of local polynomial regression
Let the random set $\{(Y_{t},X_t)\}_{t=1}^n$ follow the model:
$$Y_t=m(X_t)+\epsilon_t,\quad t\in\{1,\cdots,n\}\quad (1)$$
where $\epsilon_t$ is a random error term and $m(\cdot)$ is an unknown smooth ...
- 1,097
4
votes
2
answers
1k
views
How to create a B-spline basis without intercept and linear trend included?
I want to fit the following model using splines:
\begin{align} Y(t) = \beta_0 + \beta_1t + \sum_{j=2}^{d} \beta_jB(t)_j \end{align}
where $B_j$ are the basis functions. However, when I run the ...
2
votes
1
answer
737
views
Is Kernel-Regression parametric or non-parametric?
As the title says, is kernel regression a parametric or non-parametric method, and how can this be motivated/explained?
- 35
0
votes
1
answer
575
views
Closed form equations for simple linear regression estimators
I'm learning specifically about different forms of simple linear regression including ordinary least squares, median absolute deviation, and Theil-Sen. I have no background whatsoever in linear ...
- 89
0
votes
2
answers
170
views
can daily count data use GAM ordered categorical family, proportional-odds model?
The observed response variable Y takes on one of K(=21) ordered categories.
Here is a summary of my response data (count data: the number of hospital admission in each day), y has observations across ...
- 37
5
votes
0
answers
131
views
How can I make a prediction interval for a future response (not its mean) in regression by using bootstrap?
I'd like to know how I can use bootstrap to predict the confidence interval for a future response (not for its mean) no matter what theorical model and error distribution are, I know I can train the ...
- 1,220
1
vote
1
answer
477
views
Difference between kernel linear regression and non-parametric regression
A quick perplexity popped up in my mind while reading about non-parametric linear regression.
In linear regression, we model our response $\textbf{y} \sim \mathcal{N}(X\beta, \sigma^2I)$ so basically ...
- 637
1
vote
1
answer
365
views
What would be the interpretation of asymmetric kernels in Gaussian Process Regression?
This paper involves with asymmetric Kernels. They claim that this arises due to local parameters. But this is not really true. They induce a particular asymmetric structure in the Kernel yet still ...
- 312
0
votes
0
answers
607
views
No significant interaction in OLS, but significant in pairwise comparison
I have two independent categorical variables — (i) A: {1, 2, 3}, (ii) B: {0, 1} — with a continuous outcome variable ...
0
votes
1
answer
57
views
Validity of multilevel modeling to include results for multiple psychometric tests with subscales #statsnube
I have survey data for approx n = 1650 for multiple psychometric tests (all participants have completed all the tests), and about 12 outcome variables (from a PCA of a 52-question survey, e.g. ...
- 11
2
votes
0
answers
73
views
MCMC fitting of Dirichlet Process or Polya Tree prior to residuals in (simple linear regression)/(2-independent-samples) problem
Consider a simple location-shift semi-parametric model with two mutually-independent samples (in what follows, $F$ is a cumulative distribution function (CDF) on $\mathbb{ R }$, the $C_i$ and $T_j$ ...
- 69
13
votes
2
answers
2k
views
How to make predictions with non-parametric regression?
Let's say I have a dataset to which I have estimated a relationship using non-parametric regression, specifically Kernel (obviously in this hypothetical example it's probably overfit slightly). The ...
- 595
2
votes
2
answers
974
views
Bootstrap Standard Errors: should I divide the sampling standard deviation by $\sqrt{n}$?
Suppose I am bootstrapping an OLS regression and want the standard error of the coefficient $\beta_1$. I estimate the following regression on 1000 resamples of the data (where $B$ indexes the ...
- 103
0
votes
0
answers
106
views
Nadaraya-Watson regression alternative for binary outcome
I am looking for pointers as to what would be the non-parametric equivalent of Nadaraya-Watson regression when modelling a binary outcome. I have been googling and ended up with Generalized Additive ...
- 363
2
votes
1
answer
760
views
How can I fit a regression for a variable which have a maximum value?
Let's suppose I have a test which gives me the dosage of an analytic in the blood. The results of the assay are in a range of 0 and 1000; all subjects who have a value higher than 1000 will be ...
- 686
0
votes
1
answer
29
views
A question about regressions and estimation
I have the following regression (all variables are vectors, i.e. its multiple-regression with $n$ responses and $m$ covariates)
$$Y = a + bX + \epsilon$$
So, $Y$ is $n$-dimensional response;
$a$ is $n$...
- 1
2
votes
1
answer
854
views
KNN as a crude prototype of Gaussian Process Regression?
I've heard it said before that K-Means-Clustering is a prototypical method for Expectation-Maximization algorithm. Where KM Clustering returns a hard cluster assignment, EM returns soft assignments, ...
- 3,382
1
vote
0
answers
354
views
Is it OK to use GEE insetad of GLM for non-repeated data?
I analyse data, that are repeated (pre-post), but I work with change from baseline instead. This is a non-randomized experiment, so I was advised to run this kind of analysis bearing in mind the Lord'...
- 11
1
vote
0
answers
32
views
What is a reasonable method for two sample test on cut-off measurements?
This is a question regarding biostatistics. I am digging into some statistical analysis with SingleCellSignalR, which is a tool to predict cellular interaction with single-cell RNA-seq data. I was ...
- 11
6
votes
2
answers
296
views
Regression with flexible functional form
I am assuming a model of the form
$$Y_i=\alpha+\beta X_i+g(\mathbf{Z}_i)+\epsilon_i,$$
here $\mathbf{Z}_i$ is an $m$ dimensional vector and $\epsilon_i$ is i.i.d. white noise. I would like to ...
- 340
0
votes
0
answers
31
views
Biase of ASE estimation Kernel Regression
I'm trying to calculate the bias of the estimator $p(h)=n^{-1}\displaystyle\sum_{i=1}^{n}(Y_{j}-\hat{m}_{h}(X_{j})^{2}w(X_{j})$ of the averaged squared error. The result I find in the literature is ...
- 3
1
vote
0
answers
734
views
Alternating Conditional Expectations: Multiple regression transform
Alternating Conditional Expectations (ACE) is a non-parametric algorithm for multiple regression transform selection. It finds a set of transformed response variables that maximizes $R^2$ using ...
- 679
0
votes
1
answer
113
views
Nonparametric Regression
Suppose I have response y, continuous independent variable x and binary variable z.
...
- 357
0
votes
1
answer
76
views
How to understand the language used to describe statistics in the book "The Rise and Decline of Nations"
The tables on pages 102 - 108 are supposed to compare the growth rate and union membership between confederate and non-confederate states since 1965 (I believe it's since 1965 but it's so confusing I ...
- 103
1
vote
1
answer
810
views
How can I predict a continuous outcome variable with 1 binary and 1 ordinal predictor variable nonparametrically?
I have a binary predictor variable (situation1, situation2) and another one that's ordinally scaled (levels in an n-back task, they're called no-back,0-back,1-back & 2-back with 2-back being the ...
- 11
3
votes
1
answer
1k
views
How to interpret coefficients from rank based regression (Rfit package in R)?
I need to examine the relationship between an outcome variable (continuous) and a number of predictors. Since my data is non-normally distributed (i.e. the residuals from the multiple linear ...
- 61
1
vote
0
answers
40
views
Non asymptotic error bound for$f(x)=\mathbb{E}[Y|X=x]$
I am considering the following model:
$(X_i,Y_i)_{i=1}^n$ are iid random pairs with $X_i\in[0,1]$ and $Y_i\in\mathbf{R}$. Let $f(x)=\mathbb{E}[Y|X=x]$. Consider an estimate $\hat{f}_n$ of $f$.
Under ...
- 11
1
vote
0
answers
44
views
Alternative approach if dependent variable violates regression linearity
I am working on a research project to identify the impact of dominant personalities, and sexual esteem on sadistic behavior. I am also completely new to statistical analysis.
Both of my independent ...
- 131
0
votes
0
answers
53
views
Error $|\hat{f}_n(x)-f(x)|$ with regressogram estimator
I am learning about non parametric estimation, and more specifically about regressogram:
Let $(X_i,Y_i)_{i = 1}^n$ be a sequence of random variables in $[0,1]$ variables and $E[Y_i|X_i] = f(X_i)$. ...
- 11
2
votes
1
answer
561
views
Creating a custom distribution with flexsurvreg
I'm interested in fitting a parametric survival model but would like to explore the use of a Beta distribution for this purpose rather than a Weibull, Exponential, etc. model.
The Beta distribution ...
- 548